Mathematica Quick Reference
D. McClendon
Expression
xy
e
π
∞
Mathematica syntax
x y (don’t forget the space)
E (or use Basic Math Assistant palette)
Pi (or use Basic Math Assistant palette)
Infinity (or use Basic Math Assistant palette)
√
32
√
4
40
Sqrt[32] (or use Basic Math Assistant palette)
40^(1/4) (or use Basic Math Assistant palette)
|x − 3|
sin π
cos(x(y + 1))
cot 2π
+ 3π
3
4
arctan 1
ln 3
log6 63
log 18
27y
x−5+x2
e
Abs[x-3]
Sin[Pi]
Cos[x(y+1)]
Cot[2 Pi/3 + 3 Pi/4]
ArcTan[1]
Log[3]
Log[6,63]
Log10[18]
2^(7y) (or use Basic Math Assistant palette)
E^(x-5+x^2) or Exp[x-5+x^2]
(or use Basic Math Assistant palette)
f (x + 3) (if f is a function) f[x+3]
xf (2x) − x2 f (x)
x f[2x] - x^2 f[x]
(f ◦ g)(x)
f[g[x]]
lim f (x)
x→4
0
f (3)
000
Rg 2(x)
x dx
R5
cos x dx
2
P12
k=1
f (k)
30! (factorial)
Object
raised exponent
horizontal fraction bar
square root sign
Limit[f[x], x -> 4]
f’[3]
g’’’[x] or D[g[x],{x,3}]
Integrate[x^2,x] (or use Basic Math Assistant palette)
Integrate[Cos[x], {x, 2, 5}]
(or use Basic Math Assistant palette)
(for decimal approximation, use NIntegrate)
Sum[f[k], {k, 1, 12}]
30!
keyboard shortcut
type base, then [Control]+6, then exponent
type [Control]+/, then numerator, then [Tab], then denominator
[Control]+2
Mathematica Quick Reference
D. McClendon
Objective
To call the preceding output
Mathematica syntax
%
To get a decimal approximation to the
preceding output
N[%] (or click numerical value)
Define a function f (x) = f ormula
f[x_] = f ormula
(one equals sign, underscore after x)
Generate table of values for f
Table[{x,f[x]}, {x,xmin,xmax,step}]
Plot the graph of f (x) = f ormula
Plot[f ormula, {x,xmin,xmax}]
Plot multiple graphs at once
Plot[{f ormula,f ormula, ..., f ormula},
{x,xmin,xmax}]
Plot the graph of f (x) = f ormula
with range of y−values specified
Plot[f ormula, {x,xmin,xmax},
PlotRange -> {ymin,ymax}]
Plot the graph of f (x) = f ormula
with x- and y-axes on same scale
Plot[f ormula, {x,xmin,xmax},
PlotRange -> {ymin,ymax},
AspectRatio -> Automatic]
Find exact solution(s) to equation
of form lhs = rhs
Solve[lhs==rhs,x]
(two equals signs)
(works only with polynomials or other
relatively “easy” equations)
Find decimal approx. to solutions of
equation lhs = rhs
NSolve[lhs==rhs,x]
(two equals signs)
(works only with “easy” equations)
Find decimal approx. to solutions of
equation lhs = rhs
FindRoot[lhs==rhs,{x,guess}]
(two equals signs)
Partial fraction decomposition
Apart[ ]
Define parametric function x = f (t), y = g(t) f[t_] = {f (t),g(t)}
Plot graph of a set of parametric equations
(after defining them as f (t))
ParametricPlot[f[t], {t, -20,20},
PlotRange -> {{xmin,xmax},
{ymin,ymax}}]